There have been continuous efforts to seek for novel functional two-dimensional semiconductors with high performance for future applications in nanoelectronics and optoelectronics. In this work, we introduce a successful experimental approach to fabricate monolayer phosphorene by mechanical cleavage and the following Ar + plasma thinning process. The thickness of phosphorene is unambiguously determined by optical contrast combined with atomic force microscope (AFM). Raman spectroscopy is used to characterize the pristine and plasma-treated samples. The Raman frequency of A 2 g mode stiffens, and the intensity ratio of A 2 g to A 1 g modes shows monotonic discrete increase with the decrease of phosphorene thickness down to monolayer. All those phenomena can be used to identify the thickness of this novel two-dimensional semiconductor efficiently. This work for monolayer phosphorene fabrication and thickness determination will facilitates the research of phosphorene.

The positive refractive index of conventional optical lenses means that they need curved surfaces to form an image, whereas a negative index of refraction allows a flat slab of a material to behave as a lens and focus electromagnetic waves to produce a real image. Here we demonstrate this unique feature of imaging by a flat lens, using the phenomenon of negative refraction in a photonic crystalline material. The key advance that enabled us to make this observation lies in the design of a photonic crystal with suitable dispersion characteristics to achieve negative refraction over a wide range of angles.

We present a conjecture relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. Mathematical arguments justifying this conjecture are discussed. Numerical evidence based on computation of resonances of systems of n disks on a plane are presented supporting this conjecture. The result generalizes the Weyl law for the density of states of a closed system to chaotic open systems.PACS numbers: 05.45. Mt, 03.65.Sq, 05.45.Ac, 31.15.Gy, 95.10.Fh The celebrated Weyl law concerning the density of eigenvalues of bound states is a central result in the spectroscopy of quantum systems [1]. The Weyl formula states that the asymptotic level number N (k), defined as the number of levels with k n < k (where k → ∞) is given after smoothing by.., for a quantum system bounded in a region R of D-dimensional space whose volume is V . For closed systems with smooth boundaries, the Weyl formula is well-established, and although primarily valid in the semi-classical limit, nevertheless can be applied with astonishing accuracy to very low energies extending almost down to the ground state of integrable and chaotic closed systems. Generalizations of the Weyl law to other situations have long been sought. A notable example is the conjecture by Berry [2] for the density of states of closed systems with fractal boundaries, i.e. "fractal drums".Open systems are characterized by resonances defined by complex wavevectork n = Re(k n ) + iIm(k n ), corresponding to states with finite life times arising from escape to infinity. Open chaotic systems, which occur in a variety of physical situations, are generically characterized by a classical phase space repeller that is fractal. In this letter we present a conjecture relating the density of resonances for an open chaotic system to the fractal dimension of the associated classical repeller. It can be stated as:where d H is the partial Hausdorff dimension of the repeller [3, §4.4]. This relation generalizes the Weyl law for the density of states of a closed system to chaotic open systems.In this letter, we will provide a heuristic argument for the validity of this conjecture, and present new computations that confirm its validity.The repeller in a scattering problem is defined as the set of points in phase space which do not escape to infinity at both positive or negative times. The Hausdorff dimension of the repeller is given by D H = 2d H +2, where we did not restrict ourselves to an energy surface. For closed two dimensional systems, such as compact surfaces of constant negative curvature, we have real zeros only and N (k) = #{k n : k n ≤ k} ∼ k 2 , which is consistent with (1) as d H = 1 then everything is trapped.Our motivation comes from rigorous work on quantum resonances and in particular from the work of Sjöstrand Here we consider a different but related problem. Suppose that Z(k) is the semi-classical Selberg-Ruelle zeta function, with k the wave number. In some situations the zeros of its meromorphic continua...

We demonstrate the negative refraction of microwaves in a metallic photonic crystal prism. The spectral response of the photonic crystal prism, which manifests both positive and negative refraction, is in complete agreement with band-structure calculations and numerical simulations. The validity of Snell's law with a negative refractive index is confirmed experimentally and theoretically. The negative refraction observed corresponds to left-handed electromagnetism that arises due to the dispersion characteristics of waves in a periodic medium. This mechanism for negative refraction is different from that in metamaterials.

Materials, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. It incorporates referee's comments but changes resulting from the publishing process, such as copyediting,

Super-resolution imaging beyond Abbe's diffraction limit can be achieved by utilizing an optical medium or "metamaterial" that can either amplify or transport the decaying near-field evanescent waves that carry subwavelength features of objects. Earlier approaches at optical frequencies mostly utilized the amplification of evanescent waves in thin metallic films or metal-dielectric multilayers, but were restricted to very small thicknesses ͑Ӷ , wavelength͒ and accordingly short object-image distances, due to losses in the material. Here, we present an experimental demonstration of super-resolution imaging by a low-loss three-dimensional metamaterial nanolens consisting of aligned gold nanowires embedded in a porous alumina matrix. This composite medium possesses strongly anisotropic optical properties with negative permittivity in the nanowire axis direction, which enables the transport of both far-field and near-field components with low-loss over significant distances ͑Ͼ6 ͒, and over a broad spectral range. We demonstrate the imaging of large objects, having subwavelength features, with a resolution of at least / 4 at near-infrared wavelengths. The results are in good agreement with a theoretical model of wave propagation in anisotropic media.

Long-term memory requires activity-dependent synthesis of plasticity-related proteins (PRPs) to strengthen synaptic efficacy and consequently consolidate memory. Cytoplasmic polyadenylation element binding protein (CPEB)3 is a sequence-specific RNA-binding protein that regulates translation of several PRP RNAs in neurons. To understand whether CPEB3 plays a part in learning and memory, we generated CPEB3 knock-out (KO) mice and found that the null mice exhibited enhanced hippocampus-dependent, short-term fear memory in the contextual fear conditioning test and long-term spatial memory in the Morris water maze. The basal synaptic transmission of Schaffer collateral-CA1 neurons was normal but long-term depression evoked by paired-pulse low-frequency stimulation was modestly facilitated in the juvenile KO mice. Molecular and cellular characterizations revealed several molecules in regulating plasticity of glutamatergic synapses are translationally elevated in the CPEB3 KO neurons, including the scaffolding protein PSD95 and the NMDA receptors along with the known CPEB3 target, GluA1. Together, CPEB3 functions as a negative regulator to confine the strength of glutamatergic synapses by downregulating the expression of multiple PRPs and plays a role underlying certain forms of hippocampusdependent memories.

We show that a metamaterial consisting of aligned metallic nanowires in a dielectric matrix has strongly anisotropic optical properties. For filling ratio f < 1/2, the composite medium shows two surface plasmon resonances (SPRs): the transverse and longitudinal SPR with wavelengths λt < λ l . For λ > λ l , the longitudinal SPR, the material exhibits Re ε || < 0, Re ε ⊥ > 0, relative to the nanowires axis, enabling the achievement of broadband all-angle negative refraction and superlens imaging. An imaging theory of superlens made of these media is established. High performance systems made with Au, Ag or Al nanowires in nanoporous templates are designed and predicted to work from the infrared up to ultraviolet frequencies.PACS numbers: 72.80. Tm,78.20.Ci,42.30.Wb,78.66.Bz Since the demonstration of negative refraction (NR) [1] at microwave frequencies [2], a variety of approaches have been described to observe the phenomenon at optical frequencies [3]. There are several reasons for the interest in NR, the most prominent application being the concept of perfect lens [4] which can lead to sub-wavelength imaging beyond the diffraction limit. So far NR has been realized in periodic or quasiperiodic structures such as metamaterials [2] and photonic crystals [5][6][7].As the frequency is increased to the optical spectrum, the structure size and the unit cell size shrink to nanometer dimensions. Important developments in nanofabrication do allow the fabrication of nanostructures down to 10 nm sizes over large areas. Using either top-down nanolithography or bottom-up self assembly, it is possible to fabricate aligned nanowires in dielectric matrices with large aspect ratios. For example, in alumina nanoporous templates [8], the pore diameter can be modified between 10 to 200 nm and the thickness can be a few nanometers up to 160 µm [9]. Typical sizes of the pore diameter of 10 nm, pore distance of 50 nm can be easily obtained. Au nanowires synthesized inside the template make a uniform array of vertical nanowires arranged parallel to each other [10][11][12].In this paper we show that such aligned nanowire structures in dielectric matrices constitute a class of indefinite index media with strongly anisotropic optical properties that can be used to achieve broadband all-angle NR (AANR) and superlens imaging. We show that these anisotropic media will have two surface plasmon resonances (SPR): a longitudinal SPR and a transverse SPR. For wavelength larger than that of the longitudinal SPR, these media are negative index metamaterials and can be used for superlens imaging [4,13] in the frequency range from the deep-infrared up to the ultraviolet. NR and superlens imaging are possible due to the anisotropic optical properties. These structures do not need to be periodic. Disordered structures can also be used for NR. Example systems are designed and demonstrated. We consider a metal with Re ε m < 0 embedded in an ambient medium with positive ε a . In the long wavelength limit, one has the Bruggeman's effective medium theo...